Teachers face problems and use mathematics in ways that are distinctively
different from other mathematically-intensive professions such as engineering,
physics, economics, or nursing. The problems that teachers have to solve
demand flexible use of fundamental mathematical ideas, and fluency with
mathematical representation, language, and reasoning. We argue that careful
analysis of actual teaching practice can offer insights into the mathematical
demands of teaching. Such insights can usefully ground improvements in the
design of mathematics learning opportunities for both preservice and
experienced teachers. This session will engage participants in firsthand
experience with some of the mathematical problems that arise in teaching, and
will also offer possible directions for new designs for teacher education.

East Asian students have consistently out-performed their counterparts
around the world in international comparisons of mathematics
achievement. Can the high achievement be explained by better teaching
in the East Asian classroom? This lecture attempts to portray the
mathematics teaching in the East Asian classroom, using data from the
recently published TIMSS 1999 Video Study and a small-scale
comparative study in Hong Kong and Korea. The lecture points to the
potential of cultural factors as the underlying reasons for classroom
practice and student achievement in East Asia.

A significant minority of students are receptive to enrichment of
some sort in mathematics: they are bright, keen, and willing to be
inspired. For such students (as with others), math teachers can be a
life-changing influence. I will discuss the following important questions:
What precisely should we be telling students seeking enrichment? Should we
be giving them depth or breadth? Inspiration or knowledge? Specific tools,
or fuzzy "big pictures"? Are competitions good? Are puzzles bad? I may
also describe some of the extra-curricular programmes set up for high school
students, both here and in other countries, and relate some of the good ideas
that people have tried.

Kanwal Neel: How does a teacher make their math class interesting and
improve numeracy?

Numeracy is Not just Numbers. One must teach Number Sense, Spatial Sense,
Statistical Sense, and Sense of Relationship; Use Multiple Intelligences to
teach and learn numeracy; Make students communicate their thinking and
reasoning for any incorrect answers; Encourage discussion of mental strategies
within the curriculum, puzzles and games which require logical thinking;
Rehearse and provide development time for memorizing the "basic facts";
Activate Prior Knowledge and integrate Problem Solving; Connect Numeracy with
Literacy and other subjects; You need to create a classroom atmosphere where
the students feel secure, take risks in their learning and extend their
learning potential. Always have a POSITIVE attitude!!!